Coastal cities are exposed to multiple flood drivers such as extreme coastal high tide, storm surge, and extreme river discharge. The interaction among these flood drivers may cause compound flooding events, which could exacerbate social and economic consequences. Climate change can put greater pressure on these areas by increasing the frequency and intensity of coastal and riverine flooding. In this study, a bivariate compound flooding risk assessment method is developed to incorporate sea level rise (SLR) and nonstationary river discharge conditions. Extreme sea water level (SWL) and river stage are identified using the peak-over-threshold method, and subsequently, pairs of extremes are selected when both SWL and river stage exceed their defined thresholds within ±1 day from each other. A copula-based approach is then used to estimate the joint distribution and return period of compound coastal riverine flooding by incorporating nonstationarity into the marginal distributions of extreme SWL and river stage. The future flood risk is assessed using the notation of failure probability, which here refers to (1) the probability of occurrence of at least one major coastal or riverine flooding for a given design life (i.e., total flood risk); and (2) the probability of occurrence of at least one compound major coastal riverine flooding for a given design life (i.e., compound flood risk). Compound flood risk assessment is conducted at 26 paired NOAA-USGS stations along the Contiguous United States coast with long‐term observed data and defined flood thresholds. The results indicate that in some regions the joint return period of coastal/riverine flooding are substantially lower when considering the projected future hydroclimate conditions and SLR. The importance impact of future SLR and hydroclimate conditions is discussed regionally in terms of changes in the frequency of compound major coastal riverine flooding events.